确定大地水准面的Tikhonov最小二乘配置法

LSC法（最小二乘配置法）因能融合不同种类重力观测数据确定大地水准面的特性而受到广泛关注，但由于协方差矩阵存在病态性，微小的观测误差将被协方差矩阵的小奇异值放大，导致计算的配置结果不稳定且精度偏低。本文提出Tikhonov_LSC法，即在LSC法中引入Tikhonov正则化算法，基于GCV法选择协方差矩阵的正则化参数，利用正则化参数修正协方差矩阵的小奇异值，以抑制其对观测误差的放大影响。基于Tikhonov_LSC法计算大地水准面，能有效提高其稳定性和精度。通过以EGM2008重力场模型分别计算山区、丘陵和海域重力异常作为基础数据确定相应区域大地水准面的实验，验证了该方法的有效性。

The Tikhonov-Least Squares Collocation Method for Determining Geoid

LSC method (least squares collocation method) attracted widespread attention due to the integration of different types of gravity observation data to determine the geoid. But the observation errors are amplified by the small singular values of the ill-posed covariance matrix, leading to the unstable and low-accuracy collocation results. This paper proposed the Tikhonov-LSC method, namely in the LSC method to introduce the Tikhonov regularization algorithm, based on the GCV method to select the regularization parameter of the covariance matrix, and using the parameter to modify the small singular values of the ill-posed covariance matrix, in order to inhibit its observational error amplification impact. Using the Tikhonov_LSC method to determining the Geoid can effectively improve the stability and accuracy. The experiments using gravity anomalies based on the EGM2008 in three different regions such as mountainous region, hill and ocean region to determine the geoid verify the validity of the method.